posted by shan .
A jet starts of at a point A and is flying horizontally. And person is standing at a point B on the ground which is to the right of point A. When the jet is directly over the person, the person hears sound coming from point A. The average air temp is 20 deg C. If the speed of the plane at A is 164m/s, what is its speed at B, assuming constant acceleration? The angle between point A and the line of sight of the person on the ground is 36 deg.
Let X be the horizontal distance from A to the point above B. Let Vs be the sound speed and Vb be the plane's velocity at point B.
The time required for the plane to fly the distance X is 2X/(164 + Vb), assuming constant acceleration, since (Vb+164)/2 is the average velocity. That equals the time required for the sound to go from A to B, which is X/(Vs*cos36)
2/(164+Vb) = 1/Vs*cos36
0.809 Vs = 82 + Vb/2
Vb = 1.608 Vs -168
The sound speed is Vs = 343 m/s, so
Vb = 383 m/s
That is a lot of accleration, going from mach 0.5 to about 1.1
Angle's actually 56 degrees...